The notion of the hyperboloid at spatial infinity has been revisited
in [1]} where the definition of asymptotically
Minkowskian spacetimes at spatial infinity (AMSI) has been
introduced —see Definition REF  in Section  of the main body
of the present article. As in the analysis of [2]}, the approach in [1]} makes use of spacetime structures and,
thus, it is not geared towards the discussion of initial value
problems. However, in contrast to the definition of AEFANSI
spacetimes in [2]}, the definition of AMSI spacetimes
focuses entirely on spatial infinity and, thus, it makes no
assumptions about the properties of null infinity. A consequence of
the concept of AMSI spacetimes is the existence of a 3-dimensional
manifold \(\mathcal {H}\) , the asymptote at spatial infinity, which generalises the notion of the hyperboloid at spatial infinity.
